A362783 Square array A(n,k) = (n^(2*k + 1) + 1)/(n + 1), n >= 0, k >= 0, read by antidiagonals.
1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 11, 7, 1, 1, 1, 43, 61, 13, 1, 1, 1, 171, 547, 205, 21, 1, 1, 1, 683, 4921, 3277, 521, 31, 1, 1, 1, 2731, 44287, 52429, 13021, 1111, 43, 1, 1, 1, 10923, 398581, 838861, 325521, 39991, 2101, 57, 1, 1, 1, 43691, 3587227, 13421773, 8138021, 1439671
Offset: 0
Examples
Array begins: ===================================================================== n/k | 0 1 2 3 4 5 6 ... ----+---------------------------------------------------------------- 0 | 1 1 1 1 1 1 1 ... 1 | 1 1 1 1 1 1 1 ... 2 | 1 3 11 43 171 683 2731 ... 3 | 1 7 61 547 4921 44287 398581 ... 4 | 1 13 205 3277 52429 838861 13421773 ... 5 | 1 21 521 13021 325521 8138021 203450521 ... 6 | 1 31 1111 39991 1439671 51828151 1865813431 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
Crossrefs
Programs
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Magma
/* as array */ [[&+[(-n)^j: j in [0..2*k]]: k in [0..6]]: n in [0..6]]; // Juri-Stepan Gerasimov, May 06 2023
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PARI
A(n,k) = (n^(2*k + 1) + 1)/(n + 1) \\ Andrew Howroyd, May 03 2023
Formula
A(n,k) = Sum_{j=0..2*k} (-n)^j.
Extensions
a(49) corrected by Andrew Howroyd, Jan 20 2024